For the following problem, we are asked which of the following statements is true for $f(x,y)=x^2-2xy+y^3$
A) $f$ has all its relative extrema on the line $y=x$
B) $f$ has all its relative extrema on the parabola $x=y^2$
C) $f$ has a relative minimum at $(0,0)$
D) $f$ has an absolute minimum at $(\frac{2}{3},\frac{2}{3})$
E) $f$ has an absolute minimum at (1,1)
How would one go about solving this problem within 3 minutes?